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Clegg said "this is a government that will last." There will be "bumps and scrapes," but it will last despite those differences.
He said both men had a common purpose to give power back to people and give people more opportunity and that would make the coalition work, adding that "this is what new politics looks like." The two parties were proceeding with a very open mind, he said.
Cameron has begun appointing his first cabinet, with George Osborne as finance secretary and William Hague as foreign secretary.
Other appointments confirmed so far are Vince Cable as business secretary, Liam Fox as defense secretary and Andrew Lansley as health secretary.
Britain's Queen on Tuesday night appointed Cameron new prime minister. It is the first time the Tories and Lib Dems have had a power-sharing deal at Westminster and the first coalition in Britain since World War II.